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About Larry S

Hi there
I've had an Amex card (Amex BA rewards card) for several years.
Back in September 2015 I sent a letter to tell them I had moved house and provided our new address. However I was getting my monthly statements on line by email so did not question whether they had updated my postal address on their records.
In September 2016 I set up a standing order to cover £1000 per month payment but unbeknown to me the instruction failed.
Even though Amex had my phone number and email contact details they did not let me know payments were not being received. Instead they wrote to me at my previous address. What's important here to understand is that up until this point Amex always contacted me via their online messaging system and my overseas mobile (due to the fact we lived overseas and this was an easy and immediate way to reach us). My expectation was therefore always that if Amex needed me urgently this is how they would contact me. Amex claim they never received my letter requesting they change my address.
In January of this year (2017) I received an email from someone claiming to be a debt recovery agent for Amex. I thought it prudent to check with Amex this person was legitimate and also ascertained from Amex direct that they had cancelled my account and referred it to their debt collection agency.
I immediately paid the missing payments and have continued to pay £1000 per month whilst I decide how to move forward.
So my question is this?
Even though Amex have cancelled my account they are continuing to charge interest on the balance each month. Which means that the payment I am making is mostly going to servicing the interest. I want to clear the original amount I owe them but do not think it is fair that I should have to pay interest when my account is cancelled.
Should I talk to the debt collection agent and propose this? Or do I need to take a different approach (Ombudsman?).
All advise greatly appreciated!
Thanks in advance